论文标题
锥形奇异空间中的热内核估计值
Heat kernel estimate in a conical singular space
论文作者
论文摘要
令$（x，g）$为公制$ g = dr^2+r^2h $的产品锥，其中$ x = c（y）=（0，\ infty）_r \ times y $，交叉部分$ y $是$（n-1）$ - dimensional ofermentional ofermantional ofermantional liemannianianianian criporold $（y，h）$。我们研究与操作员$ l_v =-Δ_g+v_0 r^{ - 2} $相关的热核的上限，其中$-Δ_G$是$ x $ and $ x $ and $ v = v_0（y）的$-Δ_G$是$-Δ_G$的friedrichs扩展laplacian laplacian laplacian（y）运算符$-Δ_H+V_0+（N-2）^2/4 $是$ l^2（y）$的严格正算子。证明的新成分是$ y $的Hadamard parametrix和Wave Operator的有限传播速度。
Let $(X,g)$ be a product cone with the metric $g=dr^2+r^2h$, where $X=C(Y)=(0,\infty)_r\times Y$ and the cross section $Y$ is a $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. We study the upper boundedness of heat kernel associated with the operator $L_V=-Δ_g+V_0 r^{-2}$, where $-Δ_g$ is the positive Friedrichs extension Laplacian on $X$ and $V=V_0(y) r^{-2}$ and $V_0\in\mathcal{C}^\infty(Y)$ is a real function such that the operator $-Δ_h+V_0+(n-2)^2/4$ is a strictly positive operator on $L^2(Y)$.The new ingredient of the proof is the Hadamard parametrix and finite propagation speed of wave operator on $Y$.
